I have a vector of observations called
MyData which is a percentile score that is >= 0 and <= 1.
I would like to test the
MyData vector for normality. First I plotted the
MyData vector vs. a normal distribution with
mean= mean(mydata) and
sd = sd(mydata). In R I make the normal distribution for comparison with:
rnorm(rnorm(length(mydata), mean(mydata), sd(mydata))
Below you see the histogram and that
MyData has a higher number of observations in the middle and higher number of observations in the .8 to 1 bucket.
So the data does not look normal and when I run Jarque-Bera and Shapiro-Wilk tests I get
Jarque-Bera p value = .0007
Shapiro-Wilk p value = .000000006
so those tests also support the non-normality of the data:
My question is: can a distribution that is bounded between >= 0 and <= 1 really be tested for normality? Because as you can see from the histogram below, the normal distribution goes into ranges that
MyData does not. Note that the histogram has yellow bins that are below 0 and above 1 which are outside of the possible values of
MyData (>= 0 and <=1).
So: what would be the correct way to test for normality in this case, or am I on the right track concluding the data is not normal?